THE ANALYTICAL FUNCTION DEFINED IN THE HAMILTON-JACOBI & SCHRÖDINGER APPROACH AND THE CLASSICAL SCHRÖDINGER EQUATION

Abstract

In this paper, we show that a specific extension of the Schrödinger ansatz for two free particles, under the requirement that this function (ansatz) be analytical, is compatible with the expected physical result for a quantum description at the quantum-classical boundary; that is, its total erasure in the transition to a description compatible with classical physics.
Using the Cauchy-Riemann relation, the Laplace equation, and the Hamilton-Jacobi equation, we have shown that this function verifies a classical equation arising from the time-dependent Schrödinger equation, since in the assumed context the time variable can be taken as a parameter since it is irrelevant in the process of approximation to the quantum-classical boundary.